Deform a mesh While in animation
Most straightforward way I can think of to accomplish this:

Create a Shape Key on the car object and deform the front by hand in Edit Mode, using Proportional Editing and changing the falloff settings for a crumpled look for the front of the car. This Shape Key can be animated by hitting I while hovering over the 0.000-1.000 value to add a keyframe, and you can line it up on the Dope Sheet panel.

When the car reaches the man on the Dope Sheet timeline, the deformation Shape Key can go from 0.000 to 1.000 at the right moment. You can also &quot;drive&quot; this Shape Key with a bone or other object.